Efficient Monte Carlo characterization of quantum operations for qudits
arXiv:1404.1608 · doi:10.1103/PhysRevA.90.032317
Abstract
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number of qubits and classical computational resources that scale only polynomially in . Here, we identify the requirements for efficient Monte Carlo estimation and the corresponding properties of the measurement operator basis when replacing two-level qubits by -level qudits. Our analysis illuminates the intimate connection between mutually unbiased measurements and the existence of unitaries that can be characterized efficiently. It allows us to propose a 'hierarchy' of generalizations of the standard Pauli basis from qubits to qudits according to the associated scaling of resources required in Monte Carlo estimation of the average fidelity.
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